Fig. 2

Distribution of parameters from the multidimensional item response theory model linking estimates of latent cognitive and functional ability in the Health and Retirement Study (HRS) and the Aging, Demographics, and Memory study (ADAMS). Panel (A) shows the distribution of item loadings. The item loadings indicate the strength of the relationship between each item and the latent trait on a scale of 0–1. Panel (B) shows the distribution of item thresholds and the density distribution of estimated individual-level latent cognitive and functional abilities from the two samples overlaid in blue. Thresholds indicate either the difficulty of a binary item or the difficulty of scoring one category higher on an ordinal item. A higher number of thresholds at a given estimated ability level indicates higher precision for the estimation of the latent trait at that ability level